Toeplitz operators and weighted composition operators on variable exponent Bergman spaces

Abstract: In a paper [JFA, 278 (2020), 108401], Choe et al. obtained characterizations for bounded and compact differences of two weighted composition operators acting on standard weighted Bergman spaces over the unit disk in terms of Carleson measures. Then they extended the results to the ball setting. In this paper, we further generalize those results to variable exponent Bergman spaces over the unit ball. Our proofs, when restricted to the case of constant variable, are new and simpler. Moreover, boundedness and compactness of Toeplitz operators on variable exponent Bergman spaces are also characterized.